Forschungsgruppe "Stochastische Algorithmen und Nichtparametrische Statistik"
Seminar "Modern Methods in Applied Stochastics and Nonparametric
Statistics" Winter semester 2011/12
last reviewed: April, 25, 2012, Christine Schneider, Karsten Tabelow
18.10.2011
Speaker: tba ()
T I T L E
Abstract:
20.09.2011
Prof. Michael Tretyakov (University of Leicester)
Numerical integration of Heath-Jarrow-Morton model of interest rates
Abstract:We propose and analyze numerical methods for the Heath-Jarrow-Morton (HJM) model. To construct the methods, we first discretize the infinite dimensional HJM equation in maturity time variable using quadrature rules for approximating the arbitrage-free drift. This results in a finite dimensional system of stochastic differential equations (SDEs) which we approximate in the weak and mean-square sense using the general theory of numerical integration of SDEs. The proposed numerical algorithms are highly computationally efficient due to the use of high-order quadrature rules which allow us to take relatively large discretization steps in the maturity time without affecting overall accuracy of the algorithms. Convergence theorems for the methods are proved. Results of some numerical experiments with European-type interest rate derivatives are presented. The talk is based on a joint work with Maria Krivko (Leicester).
01.11.2011
Speaker: tba
Title
Abstract: tba
22.11.2011
Vladimir Panov (Universität Duisburg Essen)
Abelian theorem for stochastic volatility models and semiparametric estimation of the signal space
Abstract: This talk represents my PhD project. The PhD thesis handles two semiparametric statistical problems: estimation of the degree of jump activity for the affine stochastic volatility models and estimation of the signal subspace from the high-dimensional data. The purpose of the work is to improve theoretical background and to develop practical methods for solving these problems in realistic situations. By the "realistic situations" we mean the so-called low-frequency financial data for the first task and lack of "a priori" knowledge about the noisy component of the high-dimensional data for the second one.
06.12.2011
Dr. Elmar Diederichs (WIAS)
Adaptive Weights Clustering
Abstract:
13.12.2011
Jianing Zhang (WIAS)
Dual representations for general multiple stopping problems
Abstract:In this talk, we study the dual representation for generalized multiple stopping
problems, hence the pricing problem of general multiple exercise options. We derive a
dual representation which allows for cashflows which are subject to volume constraints
modeled by integer valued adapted processes and refraction periods modeled by stopping
times. As such, this extends the works by Schoenmakers [2010], Bender [2011a],
Bender [2011b], Aleksandrov and Hambly [2010] and Meinshausen and Hambly [2004]
on multiple exercise options, which either take into consideration a refraction period
or volume constraints, but not both simultaneously. We also allow more flexible cashflow
structures than the additive structure in the above references. Time permitting,
we supplement the theoretical results with an explicit Monte Carlo algorithm for constructing
confidence intervals for the price of multiple exercise options and exemplify it
by a numerical study on the pricing of a swing option in an electricity market. This talk is based on joint work with Christian Bender (Universitaet des Saarlandes) and John Schoenmakers (WIAS Berlin).
10.01.2012
Richard Metzler (University of Texas, UTSA)
Online Prediction for Simultaneous Compression & Encryption
Abstract: Because of its ability to compress and encrypt plaintext simultaneously, embedment of stream cipher rules into Elias-type entropy coders provides a fast and secure means of data compression with the ability to hide cipherstream information in the case of a known plaintext attack. Compression and security improve with continual updating of the statistical representation of the plaintext through online prediction methods. Simulations on images from a variety of classes compare the compressive and computational costs of the novel system to those of traditional compression-followed-by-encryption methods.
17.01.2012
Paul Gassiat (Université Paris Diderot, LPMA)
Optimal Investment and Consumption in a Mixed Liquid/Illiquid Market
Abstract: We study a problem of optimal investment/consumption over an infinite
horizon in a market consisting of a liquid and an illiquid asset. The
liquid asset is observed and can be traded continuously, while the
illiquid one can only be traded and observed at discrete random times
corresponding to the jumps of a Poisson process with intensity
$\lambda$.
The problem is a nonstandard mixed discrete/continuous optimal control
problem which we face by the dynamic programming approach. When the
utility has a general form we prove that the value function is the
unique viscosity solution of the HJB equation and we give a
verification theorem that describes the optimal investment strategies
for the illiquid asset. In the case of power utility, using a new
regularity result for the HJB equation via a dual approach, we are
able to solve completely the problem, finding also the optimal
consumption strategy and the optimal investment strategy for the
liquid asset. This allows us to perform
numerical simulation and to analyze the impact of the illiquidity in a
mixed market without full observation.
Based on a joint work with Salvatore Federico and Fausto Gozzi.
24.01.2012
Plamen Turkedjiev (HU Berlin)
Approximating discrete backwards stochastic differential equations using
least squares regression
Abstract: We consider the dynamic programming equation arising from the
time-discretization of backward stochastic differential equations. The
generator is assumed to be locally Lipschitz, which includes some cases
of quadratic drivers. The sequence of conditional expectations is
computed using empirical least-squares regressions. We provide full error
estimates for this approximation depending on the time-grid, the number
of simulations and the approximation spaces for regression. Furthermore,
we show that the Multi step-forward Dynamic Programming (MDP) equation
yields better error estimates than the usual One-step forward DP (ODP)
equation in the case where the generator and terminal condition are
differentiable.
This is a joint work with Emmanuel Gobet.
